Classification of unitary operators by local generatability
arXiv:2308.02728 · doi:10.1103/PhysRevB.111.085149
Abstract
Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify noninteracting unitaries in all dimensions on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence.
15 + 9 pages, 2 figures; added Appendices A.2, B.1, and E; further discussion of composition operation; published version
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